Understanding the large transverse momentum spectrum in SIDIS Nobuo - PowerPoint PPT Presentation

Understanding the large transverse momentum spectrum in SIDIS Nobuo Sato University of Connecticut SPIN18 (3D Structure of the Nucleon: TMDs) CERN, 2018 1 / 28

Kinematic regions of SIDIS 2 / 28

Kinematic regions p ⊥ h � � p + y h = 1 2 ln h p − h Current fragmentation Collinear factorization Current fragmentation Soft region Target region TMD factorization ???? Fracture functions y h Different regions are sensitive to distinct physical mechanisms 3 / 28

Theory of current fragmentation 4 / 28

Theory framework for current fragmentation small transverse W large transverse FO momentum momentum p ⊥ p ⊥ h h Current fragmentation Current fragmentation Collinear factorization Collinear factorization Current fragmentation Soft region Target region Current fragmentation Soft region Target region TMD factorization ???? Fracture functions TMD factorization ???? Fracture functions y h y h outgoing detected detected quark hadron hadron outgoing ⊗ quark ⊗ incoming quark incoming quark 5 / 28

Theory framework for current fragmentation small transverse W large transverse FO momentum momentum p ⊥ p ⊥ h h Current fragmentation Current fragmentation Collinear factorization Collinear factorization matching region Current fragmentation Soft region Target region Current fragmentation Soft region Target region TMD factorization ???? Fracture functions TMD factorization ???? Fracture functions y h ASY y h outgoing detected detected quark hadron hadron outgoing ⊗ quark ⊗ incoming quark incoming quark 6 / 28

Theory framework for current fragmentation The formulation of is based on a scale separation governed by the ratio q T /Q where z = P · p h q T = p ⊥ P · q , h /z The cross section is built as dσ = W + FO − ASY + O ( m 2 /Q 2 ) dxdQ 2 dzdp ⊥ h ∼ W for q T ≪ Q ∼ FO for q T ∼ Q 7 / 28

Why q T /Q ? (J. Gonzalez-Hernandes, T.C Rogers, NS, B. Wang) q k 1 Lets define k ≡ k 1 − q p         N Propagators in the blob        1 1 QCD ) , k 2 + O (Λ 2 k 2 + O ( Q 2 ) q Two extreme regions k 1 o | k 2 |∼ Λ 2 QCD → k is part of PDF k o | k 2 |∼ Q 2 → k is part of hard blob p | k 2 | /Q 2 is the relevant Lorentz invariant measure of transverse momentum size 8 / 28

Why q T /Q ? (J. Gonzalez-Hernandes, T.C Rogers, NS, B. Wang) In terms of partonic variables � � k 2 z q 2 � � T � = (1 − ˆ z ) + ˆ � � Q 2 Q 2 � � � For q T < Q one can write q 2 � k 2 � � 1 − q 2 � � � T T Q 2 < � < 1 − z � � Q 2 Q 2 � � � One can conclude that o q T ≪ Q signals the onset of TMD region o q T ∼ Q signals the large transverse momentum region 9 / 28

Phenomenology 10 / 28

Existing phenomenology Anselmino et al Bacchetta et al These analyzes used only W (Gaussian, CSS) Samples with q T /Q ∼ 1 . 63 has been included BUT TMDs are only valid for q T /Q ≪ 1 ! 11 / 28

Large p T SIDIS phenomenology At LO: � 1 dσ dξ e 2 � ∼ ξ − xf q ( ξ, µ ) d q ( ζ ( ξ ) , µ ) H ( ξ ) q 2 q dxdQ 2 dzdp T xz T 1 − z + x q Q 2 For collinear distributions we use o PDFs: CJ15 o FFs: DSS07 12 / 28

COMPASS: l + d → l ′ + h + + X COMPASS 17 h + 10 0 10 − 1 20 . 0 dσ dx bj dQ 2 (GeV − 2 ) vs . q T (GeV) dσ T / 10 − 2 dx bj dQ 2 dzdP 2 10 − 3 10 0 10 − 1 8 . 3 10 − 2 DDS (LO) 10 − 3 Q 2 (GeV 2 ) DDS (NLO) 2 4 6 10 0 q T > Q 10 − 1 3 . 5 10 − 2 10 − 3 2 4 6 10 0 10 − 1 1 . 8 10 − 2 10 − 3 0 . 24 < z < 0 . 30 2 4 6 10 0 0 . 30 < z < 0 . 40 10 − 1 1 . 3 10 − 2 0 . 40 < z < 0 . 50 10 − 3 0 . 65 < z < 0 . 70 2 4 6 2 4 6 2 4 6 2 4 6 2 4 6 0 . 007 0 . 010 0 . 016 0 . 03 0 . 04 0 . 07 0 . 15 0 . 27 x bj 13 / 28

COMPASS: l + d → l ′ + h + + X x bj = 0 . 13 Q 2 = 5 . 3 GeV 2 x bj = 0 . 15 Q 2 = 9 . 8 GeV 2 x bj = 0 . 29 Q 2 = 22 . 1 GeV 2 18 data / theory(LO) 14 10 6 2 data / theory(NLO) 18 0 . 24 < z < 0 . 30 0 . 30 < z < 0 . 40 14 0 . 40 < z < 0 . 50 0 . 65 < z < 0 . 70 10 q T > Q 6 2 0 20 40 0 20 40 0 20 40 q 2 T (GeV 2 ) q 2 T (GeV 2 ) q 2 T (GeV 2 ) 14 / 28

HERMES: l + p → l ′ + π + + X x bj = 0 . 04 Q 2 = 1 . 2 (GeV 2 ) x bj = 0 . 06 Q 2 = 1 . 5 (GeV 2 ) x bj = 0 . 10 Q 2 = 1 . 8 (GeV 2 ) 10 1 10 0 dx bj dQ 2 dσ < z > = 0 . 1 10 − 1 < z > = 0 . 2 T / 10 − 2 < z > = 0 . 3 dx bj dQ 2 dzdP 2 < z > = 0 . 5 x bj = 0 . 15 Q 2 = 2 . 9 (GeV 2 ) x bj = 0 . 25 Q 2 = 5 . 2 (GeV 2 ) x bj = 0 . 41 Q 2 = 9 . 2 (GeV 2 ) < z > = 0 . 9 dσ 10 1 DDS (LO) 10 0 DDS (NLO) 10 − 1 q T > Q 10 − 2 HERMES π + 0 2 4 6 0 2 4 6 0 2 4 6 q T (GeV) q T (GeV) q T (GeV) 15 / 28

HERMES: l + p → l ′ + π + + X x bj = 0 . 15 Q 2 = 2 . 9 GeV 2 x bj = 0 . 25 Q 2 = 5 . 2 GeV 2 x bj = 0 . 41 Q 2 = 9 . 2 GeV 2 data / theory(LO) 30 20 10 data / theory(NLO) < z > = 0 . 1 q T > Q < z > = 0 . 2 30 < z > = 0 . 3 < z > = 0 . 5 20 < z > = 0 . 9 10 0 20 40 0 20 40 0 20 40 q 2 T (GeV 2 ) q 2 T (GeV 2 ) q 2 T (GeV 2 ) 16 / 28

The large p T puzzle p ⊥ h ? Current fragmentation Collinear factorization Target region Current fragmentation Soft region TMD factorization ???? Fracture functions y h What are we missing? - perturtative parts : power corrections, threshold corrections - non-perturbative parts : PDFs, FFs 17 / 28

The role of non perturbative input For p T integrated @ LO: dσ � e 2 dxdQ 2 dz ∼ q f q ( x, µ ) d q ( z, µ ) q For p T differential @ LO: � 1 dσ dξ � e 2 ∼ ξ − xf q ( ξ, µ ) d q ( ζ ( ξ ) , µ ) H ( ξ ) q 2 q dxdQ 2 dzdp T xz T 1 − z + x q Q 2 Note: - gluon PDFs/FFs are involved in p T differential but not in the integrated case - For p T differential, the q T factor in the integrand provides point-by-point in q T constraints on PDF/FF - The p T spectrum is very sensitive to the shape of PDF/FF 18 / 28

Revisiting charged hadron FFs (in JAM) 19 / 28

Revisiting charged hadron FFs (in JAM) Data sets: o SIDIS ( h + , h − ) q T integrated data from COMPASS o e + e − → h ± + X (work with the 0 . 2 < z < 0 . 8 samples) o PDFs: JAM18 (see my talk at spin physics in nuclear reactions and nuclei) Extracted FFs: 3 . 0 The gluon fragmentation Q 2 = 10GeV 2 u is significantly different 2 . 5 d DSS07 → recently observed by 2 . 0 s JAM18 /D h + the NNPDF ¯ u 1 . 5 ¯ d D h + 1 . 0 ¯ s g 0 . 5 c 0 . 0 0 . 8 z 0 . 2 0 . 4 0 . 6 20 / 28

Revisiting charged hadron FFs (in JAM) 10 1 10 1 10 1 dσ dz 10 0 10 0 σ T 1 10 0 TPC TASSO 10 − 1 ALEPH 10 − 1 0 . 8 z 0 . 8 z 0 . 8 z 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 10 1 10 1 10 1 10 0 10 0 10 0 DELPHI SLD OPAL 10 − 1 0 . 8 z 0 . 8 z 0 . 8 z 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 10 1 10 1 χ 2 / npts = 0 . 53 10 0 10 0 10 − 1 10 − 1 OPAL(c) OPAL(b) 10 − 2 0 . 8 z 0 . 8 z 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 21 / 28

Revisiting charged hadron FFs (in JAM) 4 4 4 M h + + α 3 3 3 2 2 2 1 1 1 pd → h + + X 0 0 . 8 z 0 0 . 8 z 0 0 . 8 z 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 4 4 4 y ∈ [0 . 10 , 0 . 15] , α = 0 . 00 y ∈ [0 . 15 , 0 . 20] , α = 0 . 25 3 3 y ∈ [0 . 20 , 0 . 30] , α = 0 . 50 3 y ∈ [0 . 30 , 0 . 50] , α = 0 . 75 2 2 2 1 1 1 0 0 . 8 z 0 0 . 8 z 0 0 . 8 z 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 3 3 3 M h − + α 2 2 2 1 1 1 pd → h − + X 0 0 . 8 z 0 0 . 8 z 0 0 . 8 z 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 3 3 3 χ 2 / npts = 0 . 48 2 2 2 1 1 1 0 0 . 8 z 0 0 . 8 z 0 0 . 8 z 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 22 / 28

New predictions for the SIDIS q T spectrum 23 / 28

Old predictions (DSS07) @ LO 10 COMPASS 17 h + 8 6 20 . 0 4 data / theory(LO) vs . q T (GeV) 2 10 PDF : CJ15 FF : DSS07 8 6 8 . 3 4 2 Q 2 (GeV 2 ) q T > Q 10 2 4 6 8 6 3 . 5 4 2 10 2 4 6 8 6 1 . 8 4 2 10 < z > = 0 . 24 2 4 6 8 < z > = 0 . 34 6 1 . 3 4 < z > = 0 . 48 2 < z > = 0 . 68 2 4 6 2 4 6 2 4 6 2 4 6 2 4 6 0 . 007 0 . 010 0 . 016 0 . 03 0 . 04 0 . 07 0 . 15 0 . 27 x bj 24 / 28

New predictions (JAM18) @ LO 10 COMPASS 17 h + 8 6 20 . 0 4 data / theory(NLO) vs . q T (GeV) 2 10 PDF : JAM18 FF : JAM18 8 6 8 . 3 4 2 Q 2 (GeV 2 ) q T > Q 10 2 4 6 8 6 3 . 5 4 2 10 2 4 6 8 6 1 . 8 4 2 10 < z > = 0 . 24 2 4 6 8 < z > = 0 . 34 6 1 . 3 4 < z > = 0 . 48 2 < z > = 0 . 68 2 4 6 2 4 6 2 4 6 2 4 6 2 4 6 0 . 007 0 . 010 0 . 016 0 . 03 0 . 04 0 . 07 0 . 15 0 . 27 x bj 25 / 28

New predictions (JAM18) @ NLO (DDS) 10 COMPASS 17 h + 8 6 20 . 0 4 data / theory(NLO) vs . q T (GeV) 2 10 PDF : JAM18 FF : JAM18 8 6 8 . 3 4 2 Q 2 (GeV 2 ) q T > Q 10 2 4 6 8 6 3 . 5 4 2 10 2 4 6 8 6 1 . 8 4 2 10 < z > = 0 . 24 2 4 6 8 < z > = 0 . 34 6 1 . 3 4 < z > = 0 . 48 2 < z > = 0 . 68 2 4 6 2 4 6 2 4 6 2 4 6 2 4 6 0 . 007 0 . 010 0 . 016 0 . 03 0 . 04 0 . 07 0 . 15 0 . 27 x bj 26 / 28